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Any tripartite hypergraph (X 1 + X 2 + Y, E) in which | Y | = 2n – 1, the degree of each vertex y in Y is n, and the neighbor-set of y is a matching, has a matching of size n. [23] The 2n – 1 is the best possible: if | Y | = 2n – 2, then the maximum matching may be of size n-1.
[43] [2] [44] [45] By 2012, split spectrum amplitude decorrelation was shown to be effective at increasing SNR and decreasing motion artefacts. [37] Commercial OCT-A devices also emerged around this time, beginning with the OptoVue AngioVue in 2014 (SD-OCT) and the Topcon Atlantis/Triton soon after (SS-OCT). [43]
The first demonstrations of in vivo OCT imaging quickly followed. [3] [4] [5] The first US patents on OCT by the MIT/Harvard group described a time-domain OCT (TD-OCT) system. [6] [7] These patents were licensed by Zeiss and formed the basis of the first generations of OCT products until 2006.
The use of octrees for 3D computer graphics was pioneered by Donald Meagher at Rensselaer Polytechnic Institute, described in a 1980 report "Octree Encoding: A New Technique for the Representation, Manipulation and Display of Arbitrary 3-D Objects by Computer", [1] for which he holds a 1995 patent (with a 1984 priority date) "High-speed image generation of complex solid objects using octree ...
For a bipartite graph G with def(G;X) = 0, the number sur(G;X) is the largest integer s satisfying the following property for every vertex x in X: if we add s new vertices to X and connect them to the vertices in N G (x), the resulting graph has a non-negative surplus. [2]: Thm.1.3.6
The first intravascular in vivo use in a preclinical model was reported in 1994 [6] and first in human, clinical imaging in 2003. [7] The first OCT imaging catheter and system was commercialized by LightLab Imaging, Inc., a company based in Massachusetts formed following a technology transfer in 1997 from Fujimoto's lab (MIT). [8]
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Let P 1 = (X 1:Y 1:Z 1) and P 2 = (X 2:Y 2:Z 2) be two points distinct to θ. Assuming that Z 1 = Z 2 = 1 then the algorithm is given by: A = X 1 Y 2. B = Y 1 X 2. X 3 = B Y 1-Y 2 A Y 3 = X 1 A-B X 2 Z 3 = Y 2 X 2-X 1 Y 1. The cost needed is 8 multiplications and 3 additions readdition cost of 7 multiplications and 3 additions, depending on the ...